Reflections and Calculations on a Prey-Predator-Patch Problem

O. Diekmann, J. A. J. Metz and M. W. Sabelis
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O. Diekmann: Centre for Mathematics and Computer Science
J. A. J. Metz: University of Leiden, Institute of Theoretical Biology
M. W. Sabelis: University of Leiden, Department of Population Biology

A chapter in Evolution and Control in Biological Systems, 1989, pp 23-35 from Springer

Abstract: Abstract This paper is concerned with models for the interaction of plants, herbivores and their predators. We concentrate on situations in which local colonies of herbivores either over-exploit their host plant or are driven to extinction by predators. Starting from a complicated structured model, in which the local prey and predator density within patches is taken into account, we use time scale arguments to derive a three dimensional system of ordinary differential equations. The simplified system is analysed and the existence of multiple stable steady states is demonstrated.

Keywords: 92A15; physiologically structured population models; predator-preyplant interaction; patch structure; model simplification; time scale arguments; qualitative analysis; multiple stable steady states (search for similar items in EconPapers)
Date: 1989
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DOI: 10.1007/978-94-009-2358-4_4

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